Simplify the following expression: $\dfrac{7k^3}{8k^3}$ You can assume $k \neq 0$.
$ \dfrac{7k^3}{8k^3} = \dfrac{7}{8} \cdot \dfrac{k^3}{k^3} $ To simplify $\frac{7}{8}$ , find the greatest common factor (GCD) of $7$ and $8$ $7 = 7$ $8 = 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(7, 8) = = 1 $ $ \dfrac{7}{8} \cdot \dfrac{k^3}{k^3} = \dfrac{1 \cdot 7}{1 \cdot 8} \cdot \dfrac{k^3}{k^3} $ $\phantom{ \dfrac{7}{8} \cdot \dfrac{3}{3}} = \dfrac{7}{8} \cdot \dfrac{k^3}{k^3} $ $ \dfrac{k^3}{k^3} = \dfrac{k \cdot k \cdot k}{k \cdot k \cdot k} = 1 $ $ \dfrac{7}{8} \cdot 1 = \dfrac{7}{8} $